Finite Group Databasebeta

← #15930929

Subgroups — #15930929

Order 3328.

680 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118634C211yesmaximal, characteristic
2#13116327C211yesmaximal, characteristic, complemented
3#13116077C211yesmaximal, characteristic
4#13115984C211yesmaximal, characteristic, complemented
5#13115979C211yesmaximal, characteristic
6#13115768C211yesmaximal, characteristic
7#13115532C211yesmaximal, characteristic
8#13115477C211yesmaximal, characteristic, complemented
9#13115456C211yesmaximal, characteristic
10#13115456C211yesmaximal, characteristic
11#13115428C211yesmaximal, characteristic, complemented
12#13115402C211yesmaximal, characteristic, complemented
13#13115089C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2370C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×#88129C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C13×#389—21no—
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#387—21no—
24C4×C13×C4⋊C4—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718653—21no—
30#11718651—21no—
31C2×#88050C2211yescharacteristic
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718600C2211yescharacteristic
42#11718600C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718336—21no—
48#11718330—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×Dic26C2311yescharacteristic
61C13×#125—22no—
62C13×#125—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94#88129—22no—
95#88129—41no—
96C4×Dic26—22no—
97C4×Dic26—41no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88050—22no—
109#88050—22no—
110#88050—22no—
111#88050—22no—
112#88049—22no—
113#88049—22no—
114#88049—22no—
115#88049—41no—
116#88047—22no—
117#88047—41no—
118C4⋊#1055—41no—
119#88043—41no—
120#26719—131nomaximal, Sylow
121C23×D13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×Dic26—21no—
143C2×Dic26—21no—
144C2×Dic26—21no—
145C2×Dic26—21no—
146C2×Dic26—21no—
147C2×Dic26#4112yes—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4#4112yes—
160C13×C4⋊C4#4112yes—
161C13×C4⋊C4#4112yes—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—42no—
169C42×C13—81no—
170C42×C13—81no—
171#6103—42no—
172#6103—42no—
173#6103—42no—
174#6103—42no—
175#6103—81no—
176#6103—81no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181#6101—42no—
182#6101—81no—
183C4×Dic13—42no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196#2448—131no—
197#2370D1311yescharacteristic, complemented
198#2086—131no—
199#2042—131no—
200#2026—131no—
201#2025—131no—
202#1983—131no—
203#1936—131no—
204#1928—131no—
205#1925—131no—
206#1925—131no—
207#1921—131no—
208#1917—131no—
209#1863—131no—
210#1763—131no—
211C23×C13C22×D411yescharacteristic
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13H(5,𝔽2)11yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×Dic13—22no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264D52—41no—
265D52—41no—
266D52—41no—
267D52—41no—
268Dic26—22no—
269Dic26—22no—
270Dic26—41no—
271Dic26—41no—
272#1055—41no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276C2×#125C2×D1311yescharacteristic
277C2×#124—131no—
278C2×C4×Q8—131no—
279C2×#107—131no—
280C2×#107—131no—
281C2×C4⋊C8—131no—
282C2×#103—131no—
283C2×#103—131no—
284C2×#103—131no—
285C2×#103—131no—
286C2×#102—131no—
287C2×#102—131no—
288C2×#102—131no—
289C2×#102—131no—
290C2×#97—131no—
291#399—261no—
292#397—261no—
293#391—131no—
294#390—131no—
295#390—131no—
296#389—21no—
297#389—131no—
298#389C2×D1311yescharacteristic
299#389C2×D1311yescharacteristic
300#388—261no—
301#388—261no—
302#387—21no—
303#387—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4C2×D1311yescharacteristic
306C4×C4⋊C4C2×D1311yescharacteristic
307C4×C4⋊C4C2×D1311yescharacteristic
308C4×C4⋊C4C2×D1311yescharacteristic
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#336—131no—
316#336—131no—
317#336—131no—
318#336—131no—
319C22×C13#52511yescharacteristic
320C22×C13#54611yescharacteristic
321C22×C13#54811yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57511yescharacteristic
324C22×C13#57611yescharacteristic
325C22×C13#57811yescharacteristic
326C2×D13—81no—
327C2×D13—81no—
328C2×D13—81no—
329C2×D13—81no—
330C2×D13—81no—
331C2×D13—81no—
332C2×D13—81no—
333C4×C13—41no—
334C4×C13—42no—
335C4×C13—42no—
336C4×C13—41no—
337C4×C13—42no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—81no—
343C4×C13#52911yescharacteristic
344C4×C13#54211yescharacteristic
345C4×C13#55211yescharacteristic
346C4×C13#55911yescharacteristic
347Dic13—42no—
348Dic13—81no—
349Dic13—81no—
350C22×Q8—131no—
351C22×D4—131no—
352C22×C8—131no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—131no—
356#125—22no—
357#125—22no—
358#124—262no—
359#124—521no—
360C4×Q8—262no—
361C4×Q8—521no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4C22⋊D1311yescharacteristic
371C2×C4⋊C4C22⋊D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—261no—
386C2×C42C22×D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388C2×C42C22×D1311yescharacteristic
389#107—262no—
390#107—521no—
391C4⋊C8—521no—
392#103—262no—
393#103—262no—
394#103—262no—
395#103—262no—
396#102—262no—
397#102—262no—
398#102—262no—
399#102—521no—
400#97—521no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95C22⋊D1311yescharacteristic
410#95C22⋊D1311yescharacteristic
411C2×C13#245811yescharacteristic
412C2×C13#311111yescharacteristic
413C2×C13#312411yescharacteristic
414C2×C13#330911yescharacteristic
415C2×C13#332711yescharacteristic
416C2×C13#337011yescharacteristic
417C2×C13#337711yescharacteristic
418D13—161no—
419C24—261no—
420C2×Q8—132no—
421C2×Q8—261no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×D4—261no—
427C2×D4—261no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C23×D1311yescharacteristic
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—522no—
474C4⋊C4—1041no—
475C4⋊C4#612712yes—
476C4⋊C4#612712yes—
477C4⋊C4#613112yes—
478C22⋊C4—522no—
479C22⋊C4—522no—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C22⋊C4—1041no—
483C22⋊C4—1041no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—81no—
493C42—522no—
494C13#2671911yescharacteristic, complemented, Sylow
495C23—521no—
496C23—521no—
497C23—521no—
498C23—521no—
499C23—521no—
500C23—521no—
501C23—521no—
502C23C22×C22⋊D1311yescharacteristic
503Q8—262no—
504Q8—262no—
505Q8—521no—
506Q8—521no—
507D4—521no—
508D4—521no—
509D4—521no—
510D4—521no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—262no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4C2×#612711yescharacteristic
551C2×C4C2×#612711yescharacteristic
552C2×C4C2×#613111yescharacteristic
553C2×C4#8825411yescharacteristic
554C2×C4#41×D1311yescharacteristic
555C2×C4#8825611yescharacteristic
556C8—521no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—1041no—
561C22—1041no—
562C22—1041no—
563C22—1041no—
564C22—1041no—
565C22—1041no—
566C22—1041no—
567C22#1171949611yescharacteristic
568C22#1171952211yescharacteristic
569C22#1171952711yescharacteristic
570C22#1171952711yescharacteristic
571C22#1171953411yescharacteristic
572C22#1171954011yescharacteristic
573C22#1171954311yescharacteristic
574C4—41no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—522no—
585C4—1041no—
586C4—1041no—
587C4#1171928511yescharacteristic
588C4#1171928611yescharacteristic
589C4#1171928711yescharacteristic
590C4#1171929011yescharacteristic
591C2—2081no—
592C2#1311875211yescharacteristic
593C2#1312494511yescharacteristic
594C2#1312509811yescharacteristic
595C2#1312683611yescharacteristic
596C2#1312709811yescharacteristic
597C2#1312758911yescharacteristic
598C2#1312767811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2370C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2370D13
hypocenterC13#26719
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13116327C2semidirect
4. #13115984C2semidirect
8. #13115477C2semidirect
11. #13115428C2semidirect
12. #13115402C2semidirect
13. #13115089C2semidirect
14. #13114669C2semidirect
15. C13×#2370C2semidirect
197. #2370D13semidirect
494. C13#26719semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131186342
#131163272
#131160772
#131159842
#131159792
#131157682
#131155322
#131154772
#131154562
#131154282
#131154022
#131150892
#131146692
C13×#23702
#2671913